The victim, who is yet to be named, is believed to have been crushed by a large concrete column at Arena Palestra following a landslide in the area.
The man was taken to Santa Rosa hospital while six teams of firefighters provided assistance and support to other members of the construction team, who managed to escape unscathed. The construction company hired for the development, WTorre, confirmed there had been a landslide but could not release any further information about the incident.
It is the second football-related tragedy to occur in Brazil in as many days after two people were shot dead en route to Castelao Stadium in the city of Fortaleza on Sunday.
Arena Palestra was not scheduled to host any World Cup fixtures in 2014 prior to Monday's accident.